Demonstration tools for geometric properties

ABSTRACT

A variety of tools for demonstrating the mathematical properties is disclosed. In one embodiment, a demonstrator uses the tools to illuminate geometric relationships between objects in two and three-dimensional space. The tools may be a stationary exhibit or collected into a portable kit. Whether portable or stationary, the tools provide an easy to use, multi-functional, and visually captivating vehicle for demonstration of geometric properties.

PRIORITY APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 14/100,924 ('924 application), filed Dec. 9, 2013 and entitled“DEMONSTRATION TOOLS FOR GEOMETRIC PROPERTIES,” which is incorporatedherein by reference in its entirety.

The '924 application is a divisional of U.S. patent application Ser. No.12/793,677, filed Jun. 4, 2010 and entitled “DEMONSTRATION TOOLS FORGEOMETRIC PROPERTIES,” which is incorporated herein by reference in itsentirety.

FIELD OF THE DISCLOSURE

The present disclosure is directed to tools for demonstrating certainproperties of mathematical shapes, including cross-sections of geometricobjects.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an embodiment of an illumination device suitable foruse with the present disclosure.

FIG. 2 illustrates objects that may be used with the illumination deviceof FIG. 1 in some embodiments of the present disclosure.

FIG. 3 illustrates an exemplary embodiment of a system of the presentdisclosure in use by a demonstrator.

FIG. 4 illustrates a first geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 5 illustrates a second geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 6 illustrates a third geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 7 illustrates a fourth geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 8 illustrates a fifth geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 9 illustrates a sixth geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 10 illustrates a seventh geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 11 illustrates an eighth geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 12 illustrates a ninth geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 13 illustrates a tenth geometric shape capable of being presentedusing the system of the present disclosure.

FIG. 14 illustrates an eleventh geometric shape capable of beingpresented using the system of the present disclosure.

FIG. 15 illustrates an alternate embodiment of the system of the presentdisclosure.

FIGS. 16 & 17 illustrate exemplary mounting techniques to hold anillumination device on a stationary frame for use with the presentdisclosure.

FIG. 18 illustrates an irregular shape being used with the system of thepresent disclosure.

FIG. 19 illustrates an alternate mount mechanism to hold an illuminationdevice on a stationary frame.

DETAILED DESCRIPTION

Mathematics is often underappreciated for its ubiquity, beauty, andcapacity to entertain, especially amongst children. By demonstratingmathematics in an entertaining manner, understanding, and appreciationof the field may improve. The present disclosure provides a variety oftools for demonstrating the mathematical properties of physical objects,and particularly illustrates various cross-sectional views that may bemade with a variety of geometric objects. In an exemplary embodiment, alaser is used in conjunction with a translucent object to illuminate across-section of the translucent object. In a first embodiment, thelaser is positioned in fixed, stationary position and the objects areintroduced into the light projected by the laser. In a secondembodiment, the laser is a portable laser, and, together with theobjects, may be assembled into a portable kit. The orientation of theobject may be varied relative to a plane of light created by the laserto illustrate various cross-sectional slices.

The tools of the present disclosure start with an illumination device10, illustrated in FIG. 1, which in an exemplary embodiment is a laser.The illumination device 10 emits a light in a line 12 that strikes alens 14, which transforms the light of line 12 into a plane of light 16.The laser may be enclosed in a small housing. In a particularlycontemplated embodiment, the illumination device 10 and lens 14 are soldas a single unit in a preformed housing, such as the 635 nm Compact 88°Line Laser Module Diode Module as distributed by Photonic Products ofHertfordshire, UK (a copy of the data sheet can be found atwww.photonic-products.com/products/laser_diode_modules/compact/635nm_compact_88line.pdf and is hereby incorporated by reference). At 635nm, the laser emits a red light that is visible to the human eye in bothdark environs as well as reasonably well lit environs. The housing ofthe Photonic Products laser is approximately 8 mm in diameter andapproximately 29 mm in length in a generally cylindrical housing. Insome embodiments, a power source may be provided for the illuminationdevice such as a transformer coupled to a standards AC wall plug or abattery pack. In an exemplary embodiment, the laser and lens 14 arecontained within a housing 15. Alternatively, the lens 14 may be affixedto the casing of the laser. In still another embodiment, the lens 14 andthe laser are held by separate mounts, but held in a fixed relativeposition to one another (e.g., two mounts attached to a single rigidsupport member).

The second part of the tools is in the three-dimensional objects withwhich the illumination device 10 interacts. Together the illuminationdevice 10 and the three-dimensional objects form a system thateffectively illustrates cross-sectional properties of the objects. Theillustration of cross-sectional properties may be used as a prop orexhibit by teachers to educate one or more individuals about mathematicsin the form of geometric shapes in an innovative and exciting manner.Some of the objects 20 are illustrated in FIG. 2. In particular, theobjects 20 may be geometric shapes such as a cube 22, a cylinder 24, adodecahedron 26, and a cone 28. Other regular shapes such as atetrahedron, an octahedron, an icosahedron, or the like may also be usedalthough they are not illustrated. Likewise, irregular shapes (e.g.,pyramids with a square base, trapezoidal shapes, or the like) may alsobe used if desired.

In use, one or more objects 20 are introduced into the plane of light16. The plane of light 16 passes through the object 20, effectively“slicing” the object 20 and creating a virtual cross-section of theobject 20. Where the plane of light 16 intersects the object 20, thelight scatters and/or reflects so as to highlight the cross-section thatis being created.

To achieve the scattering and reflection, the objects 20 aretranslucent, such that a readily visibly discernable amount of light maypass from the illumination device 10 through the entirety of a givenobject 20. If the material used to make the objects 20 is too opaque,light throughput may suffer to the point that the plane originating onone side of the object 10 does not reach the opposite side. Conversely,if too transparent, the scattering and reflection effect created whenthe plane of light intersects with the object 20 may be less discernablethan desired. In one embodiment, the objects 20 are constructed from atransparent acrylic plastic and airbrushed with a light coat of whitelatex paint spray, such that when the paint is dry, the plastic reachesa desirable level of translucence. Alternately, a semi-transparent ortranslucent polypropylene thermoplastic may be used at the outset,eschewing the spraying step. In short, the material of the object hasenough opacity to reflect some of the light from the illumination device10, but transparent enough to allow the light to reach the other side.

In one embodiment, an object 20 may be formed from a plurality ofplastic sections that are assembled using an adhesive. For example, anassembly process may begin with a flat sheet of plastic. A router may beused to cut the sheet into smaller pieces, which may then be assembledinto a three-dimensional object 20. For example, pentagonal sides of adodecahedron may be cut from a sheet, such that all twelve sides maythen be affixed together with commercial-grade adhesive. In anotherembodiment, two or more adjacent sides of a three-dimensional object maybe cut as a single piece from the sheet. The intended intersection ofthe sides may be scored and the flat piece may be heated to a point ofpliability before folding the intersections to create two or more sidesof the three-dimensional object. For example, the six sides of a cubemay be formed from a cross or t-shape and folded into a cube. In anotherembodiment, an entire object may be constructed at once using aninjection mold and a translucent polypropylene thermoplastic polymer orsimilar material. In yet other embodiments, the three-dimensionalobjects may be made of other translucent materials, such as frostedglass.

Together, the illumination device 10 and the objects 20 may be used toillustrate mathematical properties of the objects 20. In a simpleembodiment, a single illumination device 10 may be used with an object20 as better illustrated in FIGS. 3 and 4. As illustrated, ademonstrator 30 may hold the illumination device 10 (or a housing orwand containing the illumination device 10) in one hand and an object 20in a second hand. The demonstrator 30 points the illumination device 10at the object 20. The plane of light 16 is incident on the object 20 andthereby creates a virtual cross-section, and the translucent nature ofthe object 20 means that the light reflects and scatters at the lines ofintersection such that an observer sees the virtual cross-section. Forexample, as better illustrated in FIG. 4, the plane of light 16 strikesthree surfaces of the cube 22, particularly sides 22 a, 22 b, and 22 c.This arrangement causes light to reflect along line segments 32 a, 32 b,and 32 c respectively, forming a two-dimensional triangle 33.

Given a particular object 20, and control over the relative orientationsof the object 22, the demonstrator may create and highlight differentcross-sections through the object 20. Thus, for example, a cube 22 mayprovide cross-sections of a triangle, a parallelogram, a square, and ahexagon 34 (FIG. 5). Other objects 20 may provide differentcross-sectional views.

Further exemplary cross-sectional views include the triangle 36 of thedodecahedron 26 (FIG. 6), the square 38 of the dodecahedron 26 (FIG. 7),the pentagon 40 of the dodecahedron 26 (FIG. 8), the hexagon 42 of thedodecahedron 26 (FIG. 9), or the decagon 44 of the dodecahedron 26 (FIG.10). Still further exemplary cross-sectional views include the circle 46of the cone 28 (FIG. 11), the ellipse 48 of the cone 28 (FIG. 12), theparabola 50 of the cone 28 or the hyperbola 52 of two cones 28.

In use, a single illumination device 10 may be used by a demonstrator toachieve the results illustrated herein. Alternatively, a plurality ofillumination devices 10 may also be used. The benefit of a plurality ofillumination devices 10 can be found in the fact that the linesillustrating the cross-section will be brighter and, if the illuminationdevices 10 are properly positioned, the demonstrator's hands will notinterfere with the cross-sectional lines. An example of amulti-illumination device 10 system 58 can be found in FIG. 15 whereinsix illumination devices 10 are positioned on a circular frame 60 thatforms an annulus. The circular frame 60 is mounted on a base 62. Theillumination devices 10 are spread around the interior circumference ofthe circular frame 60. While six illumination devices 10 arecontemplated, more or fewer are within the scope of the presentdisclosure. In some embodiments, the base 62 may be permanently mountedor affixed to another object (e.g., to a large wooden cart with caster,allowing the device 58 to be rolled from one location to another;directly to the floor, or the like). The frame 60 and base 62 may beconstructed from a variety of materials. In a particularly contemplatedembodiment, the frame 60 and base 62 are made from metal or wood, withthe frame 60 having an interior diameter of thirty-nine inches (99.06cm) and an exterior diameter of forty-three inches (109.22 cm). Ofcourse, frames of other shapes and sizes are within the scope of thepresent disclosure. For example, instead of a circular frame 60, apolygonal shapes or irregular shapes may be used. The size may likewisebe varied without departing from the scope of the present disclosure.While FIG. 15 illustrates the illumination devices 10 as being unequallyspaced around the frame 60, the illumination devices 10 may be spacedequidistantly around the frame 60.

In practice, the illumination devices 10 are affixed along a surface 64of the interior edge of the frame 60 and point toward the center of theframe 60 such that each illumination device 10 produces light along thesame plane (FIG. 16).

FIG. 17 illustrates an exemplary method of mounting the illuminationdevices 10 on the frame 60. In particular, an illumination device 10 ispositioned within a circular mount 66. In one embodiment, the mount 66may be made from rubber and inlaid into a circular hole drilled in theinterior side 68 of the frame 60. After being inlaid, the rubber mount66 would then hold the illumination device 10 in place. In an alternateembodiment, the mount 66 may comprise a plurality of set screws,allowing for adjustments to the x and y coordinates of the illuminationdevice 10, such that the plane of light 16 of the illumination device 60may be finely tuned so as to be co-planar with other planes of light 16case of other illumination devices 10 mounted on the frame 60.

In essence, the interior circumference of the frame 60 encloses a singleplane of light produced by the plurality of illumination devices 10. Asnoted above, the brightness of the plane of light increases with eachadditional illumination device 10. Likewise, the demonstrator's handswill not occlude all of the illumination devices 10 so that there is agreater likelihood that a desired cross-sectional view is created. Withthe plurality of illumination devices 10, it is possible to havemultiple demonstrators operating concurrently. For example, a pluralityof children may hold objects 20 within the plane of light, getting a“hands on” perspective of the experiment.

FIG. 19 illustrates an alternate embodiment of a mounting mechanism,specifically mount 80 is illustrated. Mount 80 may include a body 82,made from a metal (e.g., aluminum) or other rigid material. The body 82may be approximately two inches (5.08 cm) tall, 15/16 inch (2.38 cm)deep and wide. The body is mounted to the frame 60 with fasteners 84. Inan exemplary embodiment, two bolts are or screws are used. The body 82may be mounted on the exterior surface of the frame 60, with fasteners84 extending through the frame 60 such that the illumination device 10is flush with the interior surface 64. Illumination device 10 may sitwithin the body 82 and may have its lateral position adjusted throughthe use of set screws 86. A compression material (not shown) may bepositioned on one side of the illumination device 10 within the body 82and opposite the set screws 86 to assist in holding the illuminationdevice 10 in position. More set screws (not illustrated) may be used toassist in longitudinal positioning or the like. Use of the positioningset screws allows the illumination device 10 to be positioned in such amanner as to create the desired plane of light. Other mountingmechanisms are also within the scope of the present disclosure.

While the present disclosure has focused on creating virtualcross-section of polygons, the present disclosure is not so limited. Forexample, as illustrated in FIG. 18, a demonstrator 30 may use an object70 shaped like a human body. The demonstrator 30 may analogize thisdemonstration to an MRI or comparable medical procedure when explainingthe cross-sections created by the plane of light 16 incident on theobject 70.

Many of the above embodiments have focused on a demonstrator 30 holdingthe illumination device 10 and/or the object 20. However, in someembodiments, the illumination device 10 and/or the object 20 may bemanipulated automatically (e.g., by a computer program and/orelectro-mechanical devices in communication therewith). For example, ina specific embodiment of a stationary exhibit, a program stored withinmemory of a computer may control the illumination devices 10 held in aspecific orientation relative to a fixed object 20 such that they areactuated in series, revealing different cross-sections over the courseof an automated demonstration (e.g., stationary lasers positioned indifferent locations take turns casting planes of light throughstationary objects). Alternatively, a control system using a computerprogram may cause a robotic arm to move an illumination device 10through a choreographed set of movements that also cause differentpre-defined cross-sections to be generated on a stationary object 20. Instill another embodiment, the control system using a computer programmay cause a robotic arm to move an object 20 relative to a stationaryplane of light 16 to generate the different pre-defined cross-sections.

In yet another embodiment, such a device may also be manipulatedmanually by a demonstrator 30 (e.g., using a display screen, keyboard,mouse, joystick, and/or other devices in communication with thecomputer), who controls the timing and presentation and perhaps suppliesoral annotations or explanations. In an automated version of thepresentation, such annotations or explanations may be pre-recorded andoutput by audio speakers communicatively coupled to the computer. Inanother embodiment, multiple planes of light originating from aplurality of illumination devices 10 may pass through one or moreobjects 20 simultaneously, revealing aspects of visual and scientificinterest (e.g., two planes of light pass through a three-dimensionalobject simultaneously).

Of course, other three-dimensional objects besides those shown may beused, and other two-dimensional shapes may be demonstrated. For example,in one embodiment, a three-dimensional pyramid with a square base may beused to demonstrate a square, a trapezoid, and a parallelogram. Inanother example, a plane of light 16 may illuminate the contour ofvarious three dimensional object such as a hand or face.

Rules of Interpretation & General Definitions

Numerous embodiments are described in this disclosure, and are presentedfor illustrative purposes only. The described embodiments are not, andare not intended to be, limiting in any sense. The presently disclosedinvention(s) are widely applicable to numerous embodiments, as isreadily apparent from the disclosure. One of ordinary skill in the artwill recognize that the disclosed invention(s) may be practiced withvarious modifications and alterations, such as structural, logical,software, and electrical modifications. Although particular features ofthe disclosed invention(s) may be described with reference to one ormore particular embodiments and/or drawings, it should be understoodthat such features are not limited to usage in the one or moreparticular embodiments or drawings with reference to which they aredescribed, unless expressly specified otherwise.

The present disclosure is neither a literal description of allembodiments nor a listing of features of the invention that must bepresent in all embodiments.

Neither the Title (set forth at the beginning of the first page of thisdisclosure) nor the Abstract (set forth at the end of this disclosure)is to be taken as limiting in any way as the scope of the disclosedinvention(s).

The term “product” means any machine, manufacture and/or composition ofmatter as contemplated by 35 U.S.C. §101, unless expressly specifiedotherwise.

The terms “an embodiment”, “embodiment”, “embodiments”, “theembodiment”, “the embodiments”, “one or more embodiments”, “someembodiments”, “one embodiment” and the like mean “one or more (but notall) disclosed embodiments”, unless expressly specified otherwise.

The terms “the invention” and “the present invention” and the like mean“one or more embodiments of the present invention.”

A reference to “another embodiment” in describing an embodiment does notimply that the referenced embodiment is mutually exclusive with anotherembodiment (e.g., an embodiment described before the referencedembodiment), unless expressly specified otherwise.

The terms “including”, “comprising” and variations thereof mean“including but not limited to”, unless expressly specified otherwise.

The terms “a”, “an” and “the” mean “one or more”, unless expresslyspecified otherwise.

The term “plurality” means “two or more”, unless expressly specifiedotherwise.

The term “herein” means “in the present disclosure, including anythingwhich may be incorporated by reference”, unless expressly specifiedotherwise.

The phrase “at least one of”, when such phrase modifies a plurality ofthings (such as an enumerated list of things) means any combination ofone or more of those things, unless expressly specified otherwise. Forexample, the phrase at least one of a widget, a car and a wheel meanseither (i) a widget, (ii) a car, (iii) a wheel, (iv) a widget and a car,(v) a widget and a wheel, (vi) a car and a wheel, or (vii) a widget, acar and a wheel.

The phrase “based on” does not mean “based only on”, unless expresslyspecified otherwise. In other words, the phrase “based on” describesboth “based only on” and “based at least on”.

Where a limitation of a first claim would cover one of a feature as wellas more than one of a feature (e.g., a limitation such as “at least onewidget” covers one widget as well as more than one widget), and where ina second claim that depends on the first claim, the second claim uses adefinite article “the” to refer to the limitation (e.g., “the widget”),this does not imply that the first claim covers only one of the feature,and this does not imply that the second claim covers only one of thefeature (e.g., “the widget” can cover both one widget and more than onewidget).

Each process (whether called a method, algorithm or otherwise)inherently includes one or more steps, and therefore all references to a“step” or “steps” of a process have an inherent antecedent basis in themere recitation of the term ‘process’ or a like term. Accordingly, anyreference in a claim to a ‘step’ or ‘steps’ of a process has sufficientantecedent basis.

When an ordinal number (such as “first”, “second”, “third” and so on) isused as an adjective before a term, that ordinal number is used (unlessexpressly specified otherwise) merely to indicate a particular feature,such as to distinguish that particular feature from another feature thatis described by the same term or by a similar term. For example, a“first widget” may be so named merely to distinguish it from, e.g., a“second widget”. Thus, the mere usage of the ordinal numbers “first” and“second” before the term “widget” does not indicate any otherrelationship between the two widgets, and likewise does not indicate anyother characteristics of either or both widgets. For example, the mereusage of the ordinal numbers “first” and “second” before the term“widget” (1) does not indicate that either widget comes before or afterany other in order or location; (2) does not indicate that either widgetoccurs or acts before or after any other in time; and (3) does notindicate that either widget ranks above or below any other, as inimportance or quality. In addition, the mere usage of ordinal numbersdoes not define a numerical limit to the features identified with theordinal numbers. For example, the mere usage of the ordinal numbers“first” and “second” before the term “widget” does not indicate thatthere must be no more than two widgets.

When a single device or article is described herein, more than onedevice or article (whether or not they cooperate) may alternatively beused in place of the single device or article that is described.Accordingly, the functionality that is described as being possessed by adevice may alternatively be possessed by more than one device or article(whether or not they cooperate).

Similarly, where more than one device or article is described herein(whether or not they cooperate), a single device or article mayalternatively be used in place of the more than one device or articlethat is described. For example, a plurality of computer-based devicesmay be substituted with a single computer-based device. Accordingly, thevarious functionality that is described as being possessed by more thanone device or article may alternatively be possessed by a single deviceor article.

The functionality and/or the features of a single device that isdescribed may be alternatively embodied by one or more other devicesthat are described but are not explicitly described as having suchfunctionality and/or features. Thus, other embodiments need not includethe described device itself, but rather can include the one or moreother devices which would, in those other embodiments, have suchfunctionality/features.

Devices that are in communication with each other need not be incontinuous communication with each other, unless expressly specifiedotherwise. On the contrary, such devices need only transmit to eachother as necessary or desirable, and may actually refrain fromexchanging data most of the time. For example, a machine incommunication with another machine via the Internet may not transmitdata to the other machine for weeks at a time. In addition, devices thatare in communication with each other may communicate directly orindirectly through one or more intermediaries.

A description of an embodiment with several components or features doesnot imply that all or even any of such components and/or features arerequired. On the contrary, a variety of optional components aredescribed to illustrate the wide variety of possible embodiments of thepresent disclosure. Unless otherwise specified explicitly, no componentand/or feature is essential or required.

Further, although process steps, algorithms or the like may be describedin a sequential order, such processes may be configured to work indifferent orders. In other words, any sequence or order of steps thatmay be explicitly described does not necessarily indicate a requirementthat the steps be performed in that order. The steps of processesdescribed herein may be performed in any order practical. Further, somesteps may be performed simultaneously despite being described or impliedas occurring non-simultaneously (e.g., because one step is describedafter the other step). Moreover, the illustration of a process by itsdepiction in a drawing does not imply that the illustrated process isexclusive of other variations and modifications thereto, does not implythat the illustrated process or any of its steps are necessary to theinvention, and does not imply that the illustrated process is preferred.

Although a process may be described as including a plurality of steps,that does not indicate that all or even any of the steps are essentialor required. Various other embodiments within the scope of the describedinvention(s) include other processes that omit some or all of thedescribed steps. Unless otherwise specified explicitly, no step isessential or required.

Although a product may be described as including a plurality ofcomponents, aspects, qualities, characteristics and/or features, thatdoes not indicate that all of the plurality are essential or required.Various other embodiments within the scope of the described invention(s)include other products that omit some or all of the described plurality.

An enumerated list of items (which may or may not be numbered) does notimply that any or all of the items are mutually exclusive, unlessexpressly specified otherwise. Likewise, an enumerated list of items(which may or may not be numbered) does not imply that any or all of theitems are comprehensive of any category, unless expressly specifiedotherwise. For example, the enumerated list “a computer, a laptop, aPDA” does not imply that any or all of the three items of that list aremutually exclusive and does not imply that any or all of the three itemsof that list are comprehensive of any category.

Headings of sections provided in this disclosure are for convenienceonly, and are not to be taken as limiting the disclosure in any way.

“Determining” something can be performed in a variety of manners andtherefore the term “determining” (and like terms) includes calculating,computing, deriving, looking up (e.g., in a table, database or datastructure), ascertaining, recognizing, and the like.

A control system, as that term is used herein, may be a computerprocessor coupled with an operating system, device drivers, andappropriate programs (collectively “software”) with instructions toprovide the functionality described for the control system. The softwareis stored in an associated memory device (sometimes referred to as acomputer readable medium). While it is contemplated that anappropriately programmed general purpose computer or computing devicemay be used, it is also contemplated that hard-wired circuitry or customhardware (e.g., an application specific integrated circuit (ASIC)) maybe used in place of, or in combination with, software instructions forimplementation of the processes of various embodiments. Thus,embodiments are not limited to any specific combination of hardware andsoftware.

A “processor” means any one or more microprocessors, CPU devices,computing devices, microcontrollers, digital signal processors, or likedevices. Exemplary processors are the INTEL PENTIUM or AMD ATHLONprocessors.

The term “computer-readable medium” refers to any medium thatparticipates in providing data (e.g., instructions) that may be read bya computer, a processor or a like device. Such a medium may take manyforms, including but not limited to, non-volatile media, volatile media,and transmission media. Non-volatile media include, for example, opticalor magnetic disks and other persistent memory. Volatile media includeDRAM, which typically constitutes the main memory. Transmission mediainclude coaxial cables, copper wire and fiber optics, including thewires that comprise a system bus coupled to the processor. Transmissionmedia may include or convey acoustic waves, light waves andelectromagnetic emissions, such as those generated during RF and IR datacommunications. Common forms of computer-readable media include, forexample, a floppy disk, a flexible disk, hard disk, magnetic tape, anyother magnetic medium, a CD-ROM, DVD, any other optical medium, punchcards, paper tape, any other physical medium with patterns of holes, aRAM, a PROM, an EPROM, a FLASH-EEPROM, a USB memory stick, a dongle, anyother memory chip or cartridge, a carrier wave, or any other medium fromwhich a computer can read.

Various forms of computer readable media may be involved in carryingsequences of instructions to a processor. For example, sequences ofinstruction (i) may be delivered from RAM to a processor, (ii) may becarried over a wireless transmission medium, and/or (iii) may beformatted according to numerous formats, standards or protocols. For amore exhaustive list of protocols, the term “network” is defined belowand includes many exemplary protocols that are also applicable here.

It will be readily apparent that the various methods and algorithmsdescribed herein may be implemented by a control system and/or theinstructions of the software may be designed to carry out the processesof the present disclosure.

Where databases are described, it will be understood by one of ordinaryskill in the art that (i) alternative database structures to thosedescribed may be readily employed, and (ii) other memory structuresbesides databases may be readily employed. Any illustrations ordescriptions of any sample databases presented herein are illustrativearrangements for stored representations of information. Any number ofother arrangements may be employed besides those suggested by, e.g.,tables illustrated in drawings or elsewhere. Similarly, any illustratedentries of the databases represent exemplary information only; one ofordinary skill in the art will understand that the number and content ofthe entries can be different from those described herein. Further,despite any depiction of the databases as tables, other formats(including relational databases, object-based models, hierarchicalelectronic file structures, and/or distributed databases) could be usedto store and manipulate the data types described herein. Likewise,object methods or behaviors of a database can be used to implementvarious processes, such as those described herein. In addition, thedatabases may, in a known manner, be stored locally or remotely from adevice that accesses data in such a database. Furthermore, while unifieddatabases may be contemplated, it is also possible that the databasesmay be distributed and/or duplicated amongst a variety of devices.

As used herein a “network” is an environment wherein one or morecomputing devices may communicate with one another. Such devices maycommunicate directly or indirectly, via a wired or wireless medium suchas the Internet, Local Area Network (LAN), Wide Area Network (WAN), orEthernet (or IEEE 802.3), Token Ring, or via any appropriatecommunications means or combination of communications means. Exemplaryprotocols include but are not limited to: BLUETOOTH™, TDMA, CDMA, GSM,EDGE, GPRS, WCDMA, AMPS, D-AMPS, IEEE 802.11 (WI-FI), IEEE 802.3,TCP/IP, or the like. Note that if video signals or large files are beingsent over the network, a broadband network may be used to alleviatedelays associated with the transfer of such large files, however, suchis not strictly required. Each of the devices is adapted to communicateon such a communication means. Any number and type of machines may be incommunication via the network. Where the network is the Internet,communications over the Internet may be through a website maintained bya computer on a remote server or over an online data network includingcommercial online service providers, bulletin board systems, and thelike. In yet other embodiments, the devices may communicate with oneanother over RF, cellular networks, cable TV, satellite links, and thelike. Where appropriate encryption or other security measures such aslogins and passwords may be provided to protect proprietary orconfidential information.

Communication among computers and devices may be encrypted to insureprivacy and prevent fraud in any of a variety of ways well known in theart. Appropriate cryptographic protocols for bolstering system securityare described in Schneier, APPLIED CRYPTOGRAPHY, PROTOCOLS, ALGORITHMS,AND SOURCE CODE IN C, John Wiley & Sons, Inc. 2d ed., 1996, which isincorporated by reference in its entirety.

What is claimed is:
 1. A system comprising: an illumination devicecomprising a portable laser; and a translucent object adapted to presentvirtual cross-sections when a plane of light is projected from theillumination device onto the translucent object.
 2. The system of claim1 wherein the translucent object comprises a regular polyhedron.
 3. Thesystem of claim 1 further comprising a plurality of translucent objects.4. The system of claim 1 wherein the translucent object comprises amodel of a human body.
 5. A system comprising: a circular frame; anillumination device affixed to the circular frame; and a translucentobject adapted to present virtual cross-sections when a plane of lightis projected from the illumination device onto the translucent object.6. The system of claim 5 wherein the translucent object comprises aregular polyhedron.
 7. The system of claim 5 further comprising aplurality of translucent objects.
 8. The system of claim 5 wherein thetranslucent object comprises a model of a human body.